Assume for a moment that \(A=K\subset X\)  is compact. Based on the above-mentioned principles, one can prove by generalizing the classical Gauss variational method (see [1]}, [2]}, cf. also [3]}) that for any given \(\mu \in \mathcal {E}^+\) , there exists \(\mu ^K\in \mathcal {E}^+_K\)  uniquely determined within \(\mathcal {E}^+_K\)  by the equality \(\kappa \mu ^K=\kappa \mu \)  n.e. on \(K\) .Concerning the uniqueness, see (REF ) applied to the space \(X:=K\)  and the kernel \(\kappa ^{\prime }:=\kappa |_{K\times K}\) .
This \(\mu ^K\)  is said to be the balayage of \(\mu \in \mathcal {E}^+\)  onto (compact) \(K\) .
